A077257 Differences between two successive prime powers of prime numbers (A076707) in more than one way.

4, 168, 312, 600, 768, 792, 912, 1848, 2472, 3048, 3192, 3288, 3528, 3720, 4008, 4920, 5160, 5208, 5928, 6072, 6792, 6840, 6888, 7080, 7512, 7728, 7800, 8520, 8760, 10632, 11400, 11880, 11928, 12792, 13200, 13440, 13560, 14280, 14640, 15960

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Example

4 = 8-4 = 125-121, 168 = 529-361 = 1849-1681, 312 = 841-529 = 1681-1369.
It is interesting that 529 is a member of the last two examples.
6888 is the first one to be represented in just three ways.
4920 is the first one to be represented in four ways.

Mathematica

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^16]]]}]]]; l = Length[pp]; b = Sort[ Take[pp, -l + 1] - Take[pp, l - 1]]; Union[ b[[ Select[ Range[355], b[[ # ]] == b[[ # + 1]] &]]]]

Crossrefs

Cf. A053810, A075308, A076707, A077258.

Sequence in context: A221654 A159011 A358144 * A278124 A024265 A302453

Adjacent sequences: A077254 A077255 A077256 * A077258 A077259 A077260

Keyword

nonn

Author

Zak Seidov and Robert G. Wilson v, Oct 31 2002

Status

approved